Least Common Multiple (LCM) of 143 and 75
The least common multiple (LCM) of 143 and 75 is 10725.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 143 and 75?
First, calculate the GCD of 143 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 75 = 1 remainder 68 |
| 2 | 75 ÷ 68 = 1 remainder 7 |
| 3 | 68 ÷ 7 = 9 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 134 | 13534 |
| 173 and 36 | 6228 |
| 184 and 76 | 3496 |
| 100 and 161 | 16100 |
| 142 and 181 | 25702 |